868 
DE. EAEE ON THE CONSTETJCTION OE LIEE-TAELES. 
this value for we have ; and passing to the 
number, Putting k for the modulus of the common logarithm (>.) having 10 
Kr \y km 
k"' ' ' k~~ Kr 
for its base, we have and 
=— (1-— ; or passing to the number. 
Upon the one hypothesis, out of a generation of men an equal quantity of life* is 
destroyed in equal times, out of diminishing quantities in existence, the proportion that 
perishes of the residual life constantly increasing. 
Upon the other hypothesis, a decreasing proportion of the residual life is destroyed 
from birth down to the age of puberty ; in the after ages, a proportion increasing at 
different rates is destroyed in equal times. The quantity of life destroyed in equal times 
may be the same, or different upon this hypothesis. And in very short intervals of age 
the differences between the quantities of life destroyed may be so inconsiderable, that 
they may be neglected. 
The two hypotheses may be illustrated. Assume that at every beat of the heart an 
equal quantity of vital force on an average is consumed in excess of that produced ; or 
if this does not happen at distant ages, assume that it happens during two consecutive 
years, two consecutive days, two consecutive pulses of a generation of men, and is repre- 
sented by the deaths in the two intervals ; this will give an idea of the fii'st hj-pothesis. 
The second hypothesis will be represented by assuming that, in addition to the exist- 
ing force, a certain amount of vital force is produced, while a certain amount is also 
destroyed at every beat of the heart ; the quantity destroyed exceeding the quantity 
produced in a diminishing ratio, and then in an increasing ratio ; the proportional part 
destroyed being for this purpose always represented by the proportional number of 
hearts beating to the number of hearts ceasing to beat at every instant of age, among a 
generation of men. The respirations, the sensations, the secretions, nutrition, and all 
the vital acts may be conceived like the heart to influence the continuance of the Utal 
force ; implying here simply the force which sustains life. 
* The quality or the intensity of life at different ages is purposely left out of consideration. 
June 15, 1859. 
